The Adams spectral sequence for $U^* \left( {X,Z_p } \right)$ and applications to Lie groups, etc.

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THE ADAMS SPECTRAL SEQUENCE FOR U*(X, Zp) AND APPLICATIONS TO LIE GROUPS, ETC

1. Preliminaries. In [ l ] the structure of the weakly complex bordism of 1 connected semisimple Lie groups was studied via the Milnor, Eilenberg-Moore, Rothenberg-Steenrod sequence. See [l] for notation. In this paper we amplify the Adams spectral sequence [2], [3], [4] and relate this tool to the weakly complex cobordism theory. The techniques apply to any finite CW complex. In particular we ...

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On the unstable Adams spectral sequence for SO and U , and splittings of unstable Ext groups ∗

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The Motivic Adams Spectral Sequence

We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic 0. Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence, and use these tools to give new proofs of some results in classical algebraic topology. We also consider a m...

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My aim with these notes is to quickly get the student started with the Adams spectral sequence. To see its power requires that some concrete calculations be done. However, the algebra required can quickly become overwhelming if one starts with the generalized Adams spectral sequence. The classical Adams spectral sequence, in contrast, can be quickly set up and used to do some calculations which...

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Let E be a ring spectrum for which the E-Adams spectral sequence converges. We define a variant of Mahowald’s root invariant called the ‘filtered root invariant’ which takes values in the E1 term of the E-Adams spectral sequence. The main theorems of this paper concern when these filtered root invariants detect the actual root invariant, and explain a relationship between filtered root invarian...

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1967

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1967-11819-6